State-space models (SSMs) are a common tool for modeling multi-variate discrete-time signals. The linear-Gaussian (LG) SSM is widely applied as it allows for a closed-form solution at inference, if the model parameters are known. However, they are rarely available in real-world problems and must be estimated. Promoting sparsity of these parameters favours both interpretability and tractable inference. In this work, we propose GraphIT, a majorization-minimization (MM) algorithm for estimating the linear operator in the state equation of an LG-SSM under sparse prior. A versatile family of non-convex regularization potentials is proposed. The MM method relies on tools inherited from the expectation-maximization methodology and the iterated reweighted-l1 approach. In particular, we derive a suitable convex upper bound for the objective function, that we then minimize using a proximal splitting algorithm. Numerical experiments illustrate the benefits of the proposed inference technique.

翻译：状态空间模型（SSM）是多变量离散时间信号建模的常用工具。线性高斯（LG）SSM 因可在模型参数已知时实现封闭形式的推断而得到广泛应用。然而，在实际问题中这些参数通常难以获取，必须进行估计。促进这些参数的稀疏性既有利于可解释性，也有助于可行推断。本文提出 GraphIT，一种基于主要化-最小化（MM）算法的LG-SSM状态方程线性算子稀疏先验估计方法，并引入了一种灵活的非凸正则化势函数族。该MM方法利用了期望最大化方法论和迭代重加权-l1 算法的工具。具体而言，我们推导了目标函数的合适凸上界，并通过近端分裂算法对其进行最小化。数值实验验证了所提推断技术的优势。